In the show it's referenced in "The Prince of Winterfell" (Game of Thrones, S02E08):
DAENERYS: (TO JORAH) They are my children, and they are the only children I will ever have.
—"The Prince of Winterfell" (Game of Thrones, S02E08)
In the books it's spelled out in Mirri Maz Duur's prophecy, which the show borrows from, but admittedly omits the line that is key to this question:
"When the sun rises in the west and sets in the east," said Mirri Maz Duur. "When the seas go dry and mountains blow in the wind like leaves. When your womb quickens again, and you bear a living child. Then he will return, and not before."
In book five, A Dance With Dragons, Daenerys actually explicitly shows that she herself believes she can't have children:
There would be no son for Loraq, no heir to unite dragon and harpy. When the sun rises in the west and sets in the east, when the seas go dry and mountains blow in the wind like leaves. Only then would her womb quicken once again...
—Daenerys IV, A Dance with Dragons: A Song of Ice and Fire: Book Five
There is no specific, explicitly stated reason she can't have children (it's, in fact, possible that she may be able to bear children, but that she strongly believes Maz's prophecy due to trauma), but the witch's prophecy implies she is barren, which can be due to multiple reasons. Dany, having witnessed what her blood magic did to her son and Khal, has good reason to strongly suspect the magic also affected her ability to have children.